Q5) Three quantities are measured with uncertainties, as follows: r = 3.6 + 0.2 $ =7.8 + 0.4 1 = 1.89 + 0.13 Calculate the values and uncertainties for the following functions, using error propagation rules. Express your results in scientific notation with the correct number of significant figures. You must show all work associated with your calculations and not just the correct answer! If you don't, you'll lose points! (21 points) a) f = 3r +5st3 b) g = tVs2 -r c ) h = 2- rt 1 3 + s Q6) For the angle 0 = 3.71' + 0.13', calculate sin (0) and tan(0) and write your answers in proper form with a best estimate and uncertainty. You must show all work associated with your calculations and not just the correct answer! If you don't, you'll lose points! Also, you'll need to convert degree to radians in order to correctly calculate the uncertainties. (4 points) Page 1 of 2 PHYS 122L Spring 2023 Q7) (5 point) A simple pendulum has a length L and period 7. Suppose that you measure the period T for one value of the length L and get the results: L = (279 + 3) cm T= (3.52 + 0.02) s a) Determine the acceleration due to gravity and its associated uncertainty using error propagation. You must show all work associated with your calculations and not just the correct answer! If you don't, you'll lose points! (4 pt) b) Based on your results for part a, are you on Earth? If yes, explain a scenario that would correspond to the acceleration you found in part a. If not, determine where you might be in the solar system. Here's a link with helpful information: https:/ssdc.gsfc.nasa.gov/planetary/factsheet/ (1 pt)